The tuned vibration absorber (TVA) is a well-established passive vibration control device for achieving vibration reduction of a primary system subjected to external excitation. This contribution deals with the non-linear dynamics of an adaptive tuned vibration absorber (ATVA) with a shape memory alloy (SMA) element. Initially, a single-degree of freedom oscillator with an SMA element is analyzed showing the general characteristics of its dynamical response. Then, the analysis of an ATVA with an SMA element is carried out. Initially, small amplitude vibrations are considered in such a way that the SMA element does not undergo a stress-induced phase transformation. Under this assumption, the SMA influence is only caused by stiffness changes corresponding to temperature-induced phase transformation. Afterwards, the influence of the hysteretic behavior due to stress-induced phase transformation is considered. A proper constitutive description is employed in order to capture the general thermomechanical aspects of the SMAs. The hysteretic behavior introduces complex characteristics to the system dynamics but also changes the absorber response allowing vibration reduction in different frequency ranges. Numerical simulations establish comparisons of the ATVA results with those obtained from the classical TVA.
In this paper, we apply chaos control methods to modify bifurcations in a parametric pendulum-shaker system. Specifically, the extended time-delayed feedback control method is employed to maintain stable rotational solutions of the system avoiding period doubling bifurcation and bifurcation to chaos. First, the classical chaos control is realized, where some unstable periodic orbits embedded in chaotic attractor are stabilized. Then period doubling bifurcation is prevented in order to extend the frequency range where a period-1 rotating orbit is observed. Finally, bifurcation to chaos is avoided and a stable rotating solution is obtained. In all cases, the continuous method is used for successive control. The bifurcation control method proposed here allows the system to maintain the desired rotational solutions over an extended range of excitation frequency and amplitude.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.